I would also like to be able to run a PS2 emulator (LEGALLY, I own the games and the conosle) at a decent frame rate.

Is the PS2 emu scene really that good? I don't think they ever got that working quite as good as - say - the N64 emu scene. Even if there are half-decent PS2 emulators I guarantee you're going to need a behemoth of a computer to even run at acceptable frame-rates.

If you have a PCI-Express slot, then you shouldn't have trouble getting a nice new shiny video card.
If you have a PCI slot... you're going to need to upgrade your mobo. This can get sort of pricey because you'll almost definitely need a new CPU and RAM.

What processor do you have?

I wasn't even sure if PCI slots still existed! If you're really interested in gaming then you could save up a couple hundred more and you can put together a really nice system. As it is though, I'm not really sure it's worth buying a new videocard because a) you're not going to be able to play any recent games with it at anything under hideous settings, ergo b) you'll probably want to replace it really soon if you're into gaming.

What motherboard do you have Alec?

Most, if not all, motherboards still have PCI slots. Video cards didn't use PCI before PCI-E, they used AGP, which is missing from motherboards nowadays (for a good reason). A lot of hardware still use PCI slots for connectivity, for example sound cards and network adapters.

Yeah, I'm not sure why I said that I think I'm losing my mind or something...

But what I probably meant was PCI videocards.

Yeah I was going to say that trying to get a PCI graphics card with that money is pointless. They're horrible so don't waste the money on them.

I will say that you have absolutely no chance of emulating PS2 games on the current system even with a new video card. The emulator is more dependent on CPU than your GPU, but an upgrade in either will help somewhat. The recommended requirements to run games decently are an E8400 with an 8800GT. If you don't have at least that, games will lag, considering the fps needs to be at a stable 60 and not 30 to play smooth.

Your best chance is to buy (or build) a whole new computer. You can make one for about $500 and you'll get the results you want.

Really, you should be focusing on a CPU upgrade as well. If you don't play games as much, a CPU upgrade would be far more beneficial than a video card one. One of the entry level dual cores, and one of the more simpler motherboards could be well under $100. Grab an entry level PCIE along with it for under $100 more, and you'll have a much more capable system for handling newer games. Just move over your old RAM, HDDs, CDRom, Audio, etc, and you'll feel like you have a brand new system because you'd have upgraded the top two most important parts in video game performance.

Have your mom get you a CPU or motherboard as a gift, they're both within that range, then it will be even less for you to spend!

I recommend a AM2 motherboard with a PCIE slot, an Athlon 64 4200 X2 or 5000 X2, and a Geforce 8600 GT.

Here's a nice cheap video card - the Radeon 4650. Very nice price for the performance you get.

Cheap-ass no-frills Gigabyte motherboard. No need to spend more than you need to on a mobo. It has a PCI-E slot, 2 DDR2 RAM slots, and a slot for an Intel LGA 775 processor.
Here's a good processor - the Intel e7200. Take my word for it that it's probably the best bang-for-your-buck processor out at the moment. If you got a little extra cash I would get the e8400 for the extra 3 mb of L2 cache.
Good DDR2 RAM shit are you kidding 4 gigs for $25!? Why haven't you bought this shit yet. Actually OCZ has some good RAM too for on the cheap.

Oh yeah power supply 600w OCZ; I actually own this PSU - I got it for $25 on black friday. Works great and should get the job done for years.

So it comes to what $215 before shipping after rebates? That's a pretty solid upgrade too. That computer will smoke Portal easily. That said, if you want even more gaming horsepower you could instead get a nice video card like the Radeon 4870 or maybe the 9800 GTX+. From my experience, the NVidia video cards have a slight edge in stabillity and tend to not have driver-related heat issues. The ATI cards will most certainly give you better price to performance ratio though. If you can sneak a solid video card in your budget, you'd really be in business.